I have downloaded a free proxy server,
but proxy doesn't work, though it's a successfully tested.
What could be the reason?

There could be several reasons:

The proxy server is operational, but because it's remote from
you and the proxy is too slow, it takes quite a while for the response
to reach your PC - therefore, you think the proxy doesn't work;

Your ISP has restricted access to certain web-sites and then it has
found out your were using the proxy server to access these prohibited
web-sites. As a result, your ISP has restricted access to this proxy
server (only!) for you (only!).

The proxy server's ISP (a proxy-server is a computer connected
to the Internet, it also has its own ISP) has denied access to the proxy
server from your network (or from your ISP - for competition reasons
:-) ). In fact, there could be many reasons for this, absolutely beyond
you and not anyhow related to you;

The proxy server's settings prohibit the use of the proxy server
from your network (see item 3);

This proxy server is a corporate proxy, that means it has a list
of computers (allowed IP addresses) which are allowed to use it. In
this case, even if your neighbour uses this proxy successfully, access
to this proxy server may be closed for you;

And finally... It could be that you have set your proxy incorrectly!
These things also happen. See proxy FAQ on how
to set up a proxy server.

Conclusion: even
if a proxy server works fine with "everyone", it doesn't
mean it will work with you => there are no
100% working proxy servers that work everywhere!